Question: Rewrite as a simplified fraction. ${0.26\overline{1} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 261.1111...\\ 100x &= 26.1111...\end{align*}}$ Subtracting the two equations, we have: ${900x = 235}$ ${x = \dfrac{235}{900}} $ ${x = \dfrac{47}{180}} $